Find dy/dx by implicit differentiation. x^2-5xy+3y^2=7.

To find dy/dx by implicit differentiation.
x^2-5xy+3y^2=7.

We differentiate the function f(x,y) = C
both sides with respect to x and solve for dy/dx in terms of x and y, as y is not
explicit.

x^2-5xy +3y^2 =
7.

We differentiate both sides with respect to
x:

(x^2-5xy +3y^2)' =
(7)'.

2x-5(1y+xdy/dx) +3*2y*dy/dx =
0.

2x-5y -5xdy/dx +6ydy/dx=
0.

We collect dy/dx terms
together:

2x-5y +(-5x+6y)dy/dx =
0.

(6y-5x) dy/dx = 5y-2x.

we
divide both sides by 6y-5x.

dy/dx =
(5y-2x)/(6y-5x).

Therefore dy/dx =
(5y-2x)/(6y-5x).

Here is a video on implicit
differentiation:

https://www.youtube.com/watch?v=sL6MC-lKOrw